Ela an Eigenvalue Inequality and Spectrum Localization for Complex Matrices∗
نویسندگان
چکیده
Using the notions of the numerical range, Schur complement and unitary equivalence, an eigenvalue inequality is obtained for a general complex matrix, giving rise to a region in the complex plane that contains its spectrum. This region is determined by a curve, generalizing and improving classical eigenvalue bounds obtained by the Hermitian and skew-Hermitian parts, as well as the numerical range of a matrix.
منابع مشابه
An eigenvalue inequality and spectrum localization for complex matrices
Using the notions of the numerical range, Schur complement and unitary equivalence, an eigenvalue inequality is obtained for a general complex matrix, giving rise to a region in the complex plane that contains its spectrum. This region is determined by a curve, generalizing and improving classical eigenvalue bounds obtained by the Hermitian and skew-Hermitian parts, as well as the numerical ran...
متن کاملOn the nonnegative inverse eigenvalue problem of traditional matrices
In this paper, at first for a given set of real or complex numbers $sigma$ with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which $sigma$ is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.
متن کاملEla Generalizations of Brauer’s Eigenvalue Localization Theorem
New eigenvalue inclusion regions are given by establishing the necessary and sufficient conditions for two classes of nonsingular matrices, named double α1-matrices and double α2-matrices. These results are generalizations of Brauer’s eigenvalue localization theorem and improvements over the results in [L. Cvetković, V. Kostić, R. Bru, and F. Pedroche. A simple generalization of Geršgorin’s the...
متن کاملEla Constructions of Trace Zero Symmetric Stochastic Matrices for the Inverse Eigenvalue Problem∗
In the special case of where the spectrum σ = {λ1, λ2, λ3, 0, 0, . . . , 0} has at most three nonzero eigenvalues λ1, λ2, λ3 with λ1 ≥ 0 ≥ λ2 ≥ λ3, and λ1 + λ2 + λ3 = 0, the inverse eigenvalue problem for symmetric stochastic n × n matrices is solved. Constructions are provided for the appropriate matrices where they are readily available. It is shown that when n is odd it is not possible to re...
متن کاملEla on Nonnegative
We consider partitioned lists of real numbers Λ = {λ1, λ2, . . . , λn}, and give efficient and constructive sufficient conditions for the existence of nonnegative and symmetric nonnegative matrices with spectrum Λ. Our results extend the ones given in [R.L. Soto and O. Rojo. Applications of a Brauer theorem in the nonnegative inverse eigenvalue problem. Linear Algebra Appl., 416:844– 856, 2006....
متن کامل